That's only likely to work they are underestimating the amount of defenders each village will have. If they realize that each one usually has 100-120 militia then they are going to attack with no fewer than enough soldiers to completely overwhelm them, and unless the village happens to have very strong fortifications they are unlikely to even delay the mongols before being wiped out. For the villagers staying to defend their houses would just be suicide. Instead their best option once they realize that the mongols are coming would be to just flee or try to hide somewhere.If your force consists of 30,000 cavalry then you will not send all of them or even 1000 to attack a single village. Most like you will send 100-200 to attack a cluster of 3-4 villages. Under all caste inclusive Paik system, each village can put 100-120 militia members, if they remain in home, in house to house combat, they may put significant threat to Mongols.
Afterall Mongol forces here number only between 30,000-40,000 how long they can survive summer, militia everywhere. fortified cities, cavalry challenging them and another central army coming from Delhi?
The amount of food and provisions stored in a city or other fortified places can be a concern depending on how long the invasion lasts. If a large central army finally arrives and scares the mongols off that's good. But if the worst case scenario happens and the central army arrives after 3 months only to be outmaneuvered and defeated in a field battle, then the city now no longer has any food and is forced to surrender.
It's much safer if you can avoid having to defend a large population like that. If you have enough food stockpiled to feed the entire city plus refugees for 90 days, then if you instead kicked out all non-combatants before the siege even began, then you would have enough food feed just the garrison for potentially years.